Machine Vision and Applications

, Volume 28, Issue 3–4, pp 373–391 | Cite as

Evaluating contour segment descriptors

  • Cong Yang
  • Oliver Tiebe
  • Kimiaki Shirahama
  • Ewa Łukasik
  • Marcin Grzegorzek
Original Paper
  • 357 Downloads

Abstract

Contour segment (CS) is the fundamental element of partial boundaries or edges in shapes and images. So far, CS has been widely used in many applications, including object detection/matching and open curve matching. To increase the matching accuracy and efficiency, a variety of CS descriptors have been proposed. A CS descriptor is formed by a chain of boundary or edge points and is able to encode the geometric configuration of a CS. Because many different CS descriptors exist, a structured overview and quantitative evaluation are required in the context of CS matching. This paper assesses 27 CS descriptors in a structured way. Firstly, the analytical invariance properties of CS descriptors are explored with respect to scaling, rotation and transformation. Secondly, their distinctiveness is evaluated experimentally on three datasets. Lastly, their computation complexity is studied. Based on results, we find that both CS lengths and matching algorithms affect the CS matching performance while matching algorithms have higher affection. The results also reveal that, with different combinations of CS descriptors and matching algorithms, several requirements in terms of matching speed and accuracy can be fulfilled. Furthermore, a proper combination of CS descriptors can improve the matching accuracy over the individuals.

Keywords

Contour segment Contour segment descriptor Open curve matching Object retrieval 

Notes

Acknowledgements

Research activities leading to this work have been supported by the China Scholarship Council (CSC) and the German Research Foundation (DFG) within the Research Training Group 1564 (GRK 1564).

References

  1. 1.
    Al-Naymat, G., Chawla, S., Taheri, J.: Sparsedtw: a novel approach to speed up dynamic time warping. In: Australasian Data Mining Conference, pp. 117–127 (2009)Google Scholar
  2. 2.
    Alajlan, N., Rube, I.E., Kamel, M.S., Freeman, G.: Shape retrieval using triangle-area representation and dynamic space warping. Pattern Recogn. 40(7), 1911–1920 (2007)CrossRefMATHGoogle Scholar
  3. 3.
    Andrew, A.: Another efficient algorithm for convex hulls in two dimensions. Inf. Process. Lett. 9(5), 216–219 (1979)CrossRefMATHGoogle Scholar
  4. 4.
    Arbter, K., Snyder, W.E., Burhardt, H., Hirzinger, G.: Application of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Trans. PAMI 12(7), 640–647 (1990)CrossRefGoogle Scholar
  5. 5.
    Bai, X., Latecki, L., Liu, W.: Skeleton pruning by contour partitioning with discrete curve evolution. IEEE Trans. PAMI 29(3), 449–462 (2007)CrossRefGoogle Scholar
  6. 6.
    Baust, M., Demaret, L., Storath, M., Navab, N., Weinmann, A.: Total variation regularization of shape signals. In: IEEE CVPR, pp. 2075–2083 (2015)Google Scholar
  7. 7.
    Bellman, R.: The theory of dynamic programming. Bull. Am. Math. Soc. 60(6), 503–516 (1954)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. PAMI 24(4), 509–522 (2002)CrossRefGoogle Scholar
  9. 9.
    Bertasius, G., Shi, J., Torresani, L.: Deepedge: a multi-scale bifurcated deep network for top-down contour detection. In: IEEE CVPR, pp. 4380–4389 (2015)Google Scholar
  10. 10.
    Bhattacharyya, A.: On a measure of divergence between two multinomial populations. Indian J. Stat. 7(4), 401–406 (1946)MathSciNetMATHGoogle Scholar
  11. 11.
    Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Partial similarity of objects, or how to compare a centaur to a horse. IJCV 84(2), 163–183 (2009)CrossRefGoogle Scholar
  12. 12.
    Burkard, R.E., Dell’Amico, M., Martello, S.: Assignment Problems, Revised Reprint, pp. 93–99. SIAM (2009)Google Scholar
  13. 13.
    Chellappa, R., Bagdazian, R.: Fourier coding of image boundaries. IEEE Trans. PAMI 6(1), 102–105 (1984)CrossRefGoogle Scholar
  14. 14.
    Chen, L., Feris, R., Turk, M.: Efficient partial shape matching using smith-waterman algorithm. In: CVPR, pp. 1–6 (2008)Google Scholar
  15. 15.
    Cootes, T.F., Cooper, D., Taylor, C., Graham, J.: Trainable method of parametric shape description. Image Vis. Comput. 10(5), 289–294 (1992)CrossRefGoogle Scholar
  16. 16.
    Daliri, M.R., Torre, V.: Robust symbolic representation for shape recognition and retrieval. Pattern Recogn. 41(5), 1782–1798 (2008)CrossRefMATHGoogle Scholar
  17. 17.
    Daliri, M.R., Torre, V.: Classification of silhouettes using contour fragments. Comput. Vis. Image Underst. 113(9), 1017–1025 (2009)CrossRefGoogle Scholar
  18. 18.
    Daliri, M.R., Torre, V.: Shape recognition based on kernel-edit distance. Comput. Vis. Image Underst. 114(10), 1097–1103 (2010)CrossRefGoogle Scholar
  19. 19.
    de Junior, Mesquita Sa J.J., Backes, A.R.: Shape classification using line segment statistics. Inf. Sci. 305, 349–356 (2015)CrossRefGoogle Scholar
  20. 20.
    Donoser, M., Riemenschneider, H., Bischof, H.: Efficient partial shape matching of outer contours. In: ACCV, pp. 281–292 (2010)Google Scholar
  21. 21.
    Eitz, M., Richter, R., Boubekeur, T., Hildebrand, K., Alexa, M.: Sketch-based shape retrieval. ACM Graph. 31(4), 1–10 (2012)Google Scholar
  22. 22.
    Fawcett, T.: An introduction to roc analysis. Pattern Recogn. Lett. 27(8), 861–874 (2006)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ferrari, V., Tuytelaars, T., Gool, L.V.: Object detection by contour segment networks. In: ECCV, pp. 14–28 (2006)Google Scholar
  24. 24.
    Hariharan, B., Arbelaez, P., Girshick, R., Malik, J.: Hypercolumns for object segmentation and fine-grained localization. In: Mortensen, E., Fidler, S. (eds.) IEEE CVPR, pp. 447–456 (2015)Google Scholar
  25. 25.
    Harris, J.W., Stocker, H.: Segment of a circle. In: Stocker, H. (ed.) Handbook of Mathematics and Computational Science, pp. 92–93. Springer, New York, USA (1998)CrossRefGoogle Scholar
  26. 26.
    Homer, S., Selman, A.: Introduction to complexity theory. In: Gries, D., Schneider, FB. (eds.) Computability and Complexity Theory. Texts in Computer Science, pp. 75–80. Springer, New York, USA (2011)Google Scholar
  27. 27.
    Karczmarek, P., Kiersztyn, A., Pedrycz, W., Rutka, P.: Chain code-based local descriptor for face recognition. In: CORES, pp. 10–20 (2015)Google Scholar
  28. 28.
    Kauppinen, H., Seppanen, T., Pietikainen, M.: An experimental comparison of autoregressive and fourier-based descriptors in 2d shape classification. IEEE Trans. PAMI 17(2), 201–207 (1995)CrossRefGoogle Scholar
  29. 29.
    Kontschieder, P., Riemenschneider, H., Donoser, M., Bischof, H.: Discriminative learning of contour fragments for object detection. In: BMVC, pp. 1–12 (2011)Google Scholar
  30. 30.
    Krzyzak, A., Leung, S., Suen, C.: Reconstruction of two-dimensional patterns from fourier descriptors. Mach. Vis. Appl. 2(3), 123–140 (1989)CrossRefGoogle Scholar
  31. 31.
    Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2, 83–97 (1955)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Kurtzberg, J.M.: On approximation methods for the assignment problem. J. ACM 9(4), 419–439 (1962)MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Latecki, L.J., Lakamper, R., Eckhardt, T.: Shape descriptors for non-rigid shapes with a single closed contour. In: Werner, B. (ed.) IEEE CVPR, pp. 424–429. IEEE Computer Society, Los Alamitos, CA, USA (2000)Google Scholar
  34. 34.
    Liu, L., Shell, D.: Assessing optimal assignment under uncertainty: an interval-based algorithm. In: Ayanian, N., Kuindersma, S. (eds.) Robotics: Science and Systems. The MIT Press, Cambridge, MA USA (2010)Google Scholar
  35. 35.
    Liu, Y., Gall, J., Stoll, C., Dai, Q., Seidel, H.P., Theobalt, C.: Markerless motion capture of multiple characters using multiview image segmentation. IEEE Trans. PAMI 35(11), 2720–2735 (2013)CrossRefGoogle Scholar
  36. 36.
    Lu, C., Latecki, L., Adluru, N., Yang, X., Ling, H.: Shape guided contour grouping with particle filters. In: IEEE ICCV, pp. 2288–2295 (2009)Google Scholar
  37. 37.
    Ma, T., Latecki, L.: From partial shape matching through local deformation to robust global shape similarity for object detection. In: IEEE CVPR, pp. 1441–1448 (2011)Google Scholar
  38. 38.
    Ma, T., Latecki, L.J.: From partial shape matching through local deformation to robust global shape similarity for object detection. In: IEEE CVPR, pp. 1441–1448 (2011)Google Scholar
  39. 39.
    Maheshwari, A., Sack, J.R., Shahbaz, K., Zarrabi-Zadeh, H.: Improved algorithms for partial curve matching. Algorithmica 69(3), 641–657 (2014)MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Ohm, J.R., Bunjamin, F., Liebsch, W., Makai, B., Mller, K., Smolic, A., Zier, D.: A set of visual feature descriptors and their combination in a low-level description scheme. Sig. Process. Image Commun. 16(12), 157–179 (2000)CrossRefGoogle Scholar
  41. 41.
    Otsu, N.: A threshold selection method from gray-level histograms. Automatica 11(285–296), 23–27 (1975)Google Scholar
  42. 42.
    Payet, N., Todorovic, S.: From a set of shapes to object discovery. In: ECCV, pp. 57–70 (2010)Google Scholar
  43. 43.
    Peura, M., Iivarinen, J.: Efficiency of simple shape descriptors. In: Aspects of visual form, pp. 443–451 (1997)Google Scholar
  44. 44.
    Plackett, R.L.: Karl Pearson and the chi-squared test. Int. Stat. Rev. 51(1), 5972 (1983)MathSciNetCrossRefMATHGoogle Scholar
  45. 45.
    Riemenschneider, H., Donoser, M., Bischof, H.: Using partial edge contour matches for efficient object category localization. In: ECCV, pp. 29–42 (2010)Google Scholar
  46. 46.
    Rubner, Y., Tomasi, C., Guibas, L.J.: The earth mover’s distance as a metric for image retrieval. IJCV 40(2), 99–121 (2000)CrossRefMATHGoogle Scholar
  47. 47.
    Salvador, S., Chan, P.: Fastdtw: toward accurate dynamic time warping in linear time and space. In: KDD, pp. 70–80 (2004)Google Scholar
  48. 48.
    Sellers, P.H.: The theory and computation of evolutionary distances: pattern recognition. J. Algorithms 1(4), 359–373 (1980)MathSciNetCrossRefMATHGoogle Scholar
  49. 49.
    Shotton, J., Blake, A., Cipolla, R.: Multiscale categorical object recognition using contour fragments. IEEE Trans. PAMI 30(7), 1270–1281 (2008)CrossRefGoogle Scholar
  50. 50.
    Shu, X., Wu, X.J.: A novel contour descriptor for 2d shape matching and its application to image retrieval. Image Vis. Comput. 29(4), 286–294 (2011)CrossRefGoogle Scholar
  51. 51.
    Thureson, J., Carlsson, S.: Appearance based qualitative image description for object class recognition. In: ECCV, pp. 518–529 (2004)Google Scholar
  52. 52.
    Tieng, Q.M., Boles, W.: Recognition of 2d object contours using the wavelet transform zero-crossing representation. IEEE Trans. PAMI 19(8), 910–916 (1997)CrossRefGoogle Scholar
  53. 53.
    van de Sande, K., Gevers, T., Snoek, C.: Evaluating color descriptors for object and scene recognition. IEEE Trans. PAMI 32(9), 1582–1596 (2010)CrossRefGoogle Scholar
  54. 54.
    Van Otterloo, P.J.: A Contour-Oriented Approach to Shape Analysis. Prentice Hall International Ltd., Hertfordshire (1991)MATHGoogle Scholar
  55. 55.
    Wang, F., Kang, L., Li, Y.: Sketch-based 3d shape retrieval using convolutional neural networks. In: IEEE CVPR, pp. 1875–1883 (2015)Google Scholar
  56. 56.
    Wang, J., Bai, X., You, X., Liu, W., Latecki, L.J.: Shape matching and classification using height functions. PR Lett. 33(2), 134–143 (2012)Google Scholar
  57. 57.
    Wang, X., Feng, B., Bai, X., Liu, W., Jan Latecki, L.: Bag of contour fragments for robust shape classification. Pattern Recogn. 47(6), 2116–2125 (2014)CrossRefGoogle Scholar
  58. 58.
    Yang, C., Tiebe, O., Pietsch, P., Feinen, C., Kelter, U., Grzegorzek, M.: Shape-based object retrieval by contour segment matching. In: IEEE ICIP, pp. 2202–2206 (2014)Google Scholar
  59. 59.
    Yang, C., Tiebe, O., Pietsch, P., Feinen, C., Kelter, U., Grzegorzek, M.: Shape-based object retrieval and classification with supervised optimisation. In: ICPRAM, pp. 204–211 (2015)Google Scholar
  60. 60.
    Yang, H.S., Lee, S.U., Lee, K.M.: Recognition of 2d object contours using starting-point-independent wavelet coefficient matching. VCIR 9(2), 171–181 (1998)Google Scholar
  61. 61.
    Yang, M., Kpalma, K., Idiyo, R.J.: A survey of shape feature extraction techniques. In: Pattern Recognition, pp. 43–90 (2008)Google Scholar
  62. 62.
    Young, I.T., Walker, J.E., Bowie, J.E.: An analysis technique for biological shape. I. Inf. Control 25(4), 357–370 (1974)MathSciNetCrossRefMATHGoogle Scholar
  63. 63.
    Yule, G., Kendall, M.: An Introduction to the Theory of Statistic, 14th edn. Griffin, London, UK (1968)MATHGoogle Scholar
  64. 64.
    Zhang, D., Lu, G.: Review of shape representation and description techniques. Pattern Recogn. 37(1), 1–19 (2004)CrossRefGoogle Scholar
  65. 65.
    Zhu, Q., Wang, L., Wu, Y., Shi, J.: Contour context selection for object detection: a set-to-set contour matching approach. In: ECCV, pp. 774–787 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Cong Yang
    • 1
  • Oliver Tiebe
    • 1
  • Kimiaki Shirahama
    • 1
  • Ewa Łukasik
    • 2
  • Marcin Grzegorzek
    • 1
    • 3
  1. 1.Research Group for Pattern Recognition, Institute for Vision and GraphicsUniversity of SiegenSiegenGermany
  2. 2.Laboratory of Operational Research and Artificial IntelligenceInstitute of Computing Science, Poznan University of TechnologyPoznanPoland
  3. 3.Faculty of Informatics and CommunicationUniversity of Economics in KatowiceKatowicePoland

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